Work

Overlap locking and nonperturbative effects in spin glasses

Year: 2026

Type: article

Abstract: We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this effect depends on the strength of the coupling between the two systems. Nonperturbative phenomena are present when [Formula: see text], being [Formula: see text] the coupling Hamiltonian and [Formula: see text] the system size. In this intermediate-coupling region, the effect is related to finite-size free-energy corrections in mean-field spin-glass models and to correlations in the Dyson hierarchical spin glass, a model that mimics the physics of finite-dimensional systems. We study this phenomenon in the mean-field approach, both analytically and numerically, and we finally compute the critical exponents for finite-volume corrections in mean-field theory and for the decay of correlations in the Dyson hierarchical model.

Source: Proceedings of the National Academy of Sciences

DOI: 10.1073/pnas.2606171123

Authors: Silvio Franz, Giorgio Parisi, Federico Ricci-Tersenghi